J. Aust. Math. Soc.  79 (2005), 131-140

Some questions about rotundity and renormings in Banach spaces

A. Aizpuru   Departamento de Matemáticas   Facultad de Ciencias   Universidad de Cádiz   Polígono Río San Pedro   11.510 Puerto Real (Cádiz)   Spain   antonio.aizpuru@uca.es and F. J. Garcia-Pacheco   Departamento de Matemáticas   Facultad de Ciencias   Universidad de Cádiz   Polígono Río San Pedro   11.510 Puerto Real (Cádiz)   Spain   fjavier.garcia@uca.es

Abstract

In this paper, we show some results involving classical geometric concepts. For example, we characterize rotundity and Efimov-Stechkin property by mean of faces of the unit ball. Also, we prove that every almost locally uniformly rotund Banach space is locally uniformly rotund if its norm is Fréchet differentiable. Finally, we also provide some theorems in which we characterize the (strongly) exposed points of the unit ball using renormings.

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